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We consider near-critical planar systems with boundary conditions inducingphase separation. While order parameter correlations decay exponentially inpure phases, we show by direct field theoretical derivation how phaseseparation generates long range correlations in the direction parallel to theinterface, and determine their exact analytic form. The latter leads tospecific contributions to the structure factor of the interface.

Long range correlations generated by phase separation. Exact results from field theory